Question

Three diagonal of a rhombus are 16cm and 12cm. Find the length of each side of the rhombus.

Answer 1

We know that,

Diagonals of Rhombus bisects each other at 90°

So,

<AOB = 90°

AO = AC /2 = 12 /2 = 6 cm

BO = BD / 2 = 16 / 2 = 8 cm

Now,

In Triangle AOB,

By Pythagoras theoram

AB^2 = AO^2 +BO^2

=> AB^2 = ( 6)^2 + (8)^2

=> AB^2 = 36 + 64

=> AB^2 = 100

=> AB = 10 cm

Side of Rhombus = 10 cm

Answer 2

Correction in your question,

"Two " is written wrong as "three".

____________

Now,

As we know that diagonals of rhombus bisects each other at 90°.

Then, by Pythagoras theorem,

(Half of first diagonal)²+(half of second diagonal)² = side²


(16/2)² +(12/2)² = side²

(8)² +(6)² = side²

64 + 36=side²

100 = side²


√100 = side

10 = side of rhombus


Lenght of each side of rhombus is 10cm




I hope this will help you



-by ABHAY